2015 IEEE PES Innovative Smart Grid Technologies Latin America (ISGT LATAM)
A A Method Applied in Multifunctional Single−Phase
Solar Inverters
Lucas S. Xavier
Allan F. Cupertino
Heverton A. Pereira
Gerência de Especialistas em
Sistemas Elétricos de Potência
Universidade Federal de Viçosa
Av. P. H. Rolfs s/n, 36570-000
Viçosa, Brazil
Email: lsantx@gmail.com
Centro Federal de Educação
Tecnológica de Minas Gerais
Av. Amazonas 5253, 30421-169
Belo Horizonte, Brazil
Email: allan.cupertino@yahoo.com.br
Gerência de Especialistas em
Sistemas Elétricos de Potência
Universidade Federal de Viçosa
Av. P. H. Rolfs s/n, 36570-000
Viçosa, Brazil
Email: heverton.pereira@ufv.br
Abstract—The inverter multifunctional operation is an interesting concept to improve the power quality index of an
installation. This approach is based on the harmonic current
compensation, generated by nonlinear loads. An important issue
for the multifunctional operation is the harmonic detection
method. The traditional methods detects all harmonic contents
of the load current and the control tuning tends to be complex
and few flexible, once the load harmonic contents are not well
defined. Therefore, this work proposes a novel adaptive current
harmonic detection method applied in multifunctional singlephase photovoltaic inverters. The proposed strategy is frequency
adaptive and able to detect the load harmonic current with higher
amplitude. This method consists in a cascade association of two
phase-locked loop based on second order generalized integrator
(SOGI-PLL). Simulation results show performance of the current
harmonic detection method proposed, improving significantly
the grid current quality just compensating the higher harmonic
contents.
I. I NTRODUCTION
The photovoltaic (PV) plants have experienced a high
expansion in the worldwide electrical systems in the last
years [1]. For this reason, special attention has been paid by
researchers in relation to reliability and efficiency of gridconnected photovoltaic systems [2]. The important element
in PV systems are the solar inverters. These elements are
responsible to extract the maximum power from photovoltaic
plant and inject it into the grid [3]. Furthermore, due to
variations in solar irradiance, the PV inverters have potential
to improve the power quality index at the point of common
coupling (PCC) [3], [4], [5], [6].
An interesting mode to improving the power quality index
of an installation by means of PV system is aggregating
to the inverter control strategy ancillary services, such as,
current harmonic compensation. It transforms the inverter in
a multifunctional device [3], [6].
In multifunctional operation, the current harmonic detection method is an important issue. However, most proposed
methods are not capable to detect the predominant harmonic
component frequency [7], [8], [9], [10], [11]. This strategy
978-1-4673-6605-2/15/$31.00 ©2015 IEEE
can be interesting in order to compensate only the current
harmonic component with higher amplitude. Thereby, the current controller can be tuned for specific harmonics, increasing
efficiency and reducing the control algorithm complexity. The
issue on harmonic selectivity has been approached in some
works in the literature [12], [13].
In single-phase applications, many works use proportionalresonant (PR) control [14], [15] because the current loop
references are sinusoidal. However, PR controller can compensate only one frequency. Therefore, one resonant controller
needs to be designed for each harmonic frequency [15]. This
fact increases the control algorithm complexity. When the
current harmonic contents of a load are not well defined,
the proportional-integral (PI) controllers can be an interesting
solution. However, with many harmonic orders, the PI controller has steady state error due to its limited current tracking
capability.
In this context, this work proposes a novel adaptive current
harmonic detection method applied in a single-phase multifunctional inverter able to detect the load current harmonic
component with higher amplitude. This detection method
consists in a cascade association of two phase-locked loop
based on a second order generalized integrator (SOGI-PLL)
proposed in [16].
This proposed detection method is based on the adaptive characteristic of the second order generalized integrator
(SOGI) [16], [17]. The SOGI can be tuned by feedback of
the detected frequency. Some works use the SOGI feedback
to make it adaptive under distorted grid conditions [9], [18].
The novel detection method is applied in a single-phase
PV system as shown in Fig. 1. The control system is based
on a linear PI control. Electrical model of the solar panel
proposed in [19] is used. An algorithm of maximum power
point tracking (MPPT) calculates the reference of dc-bus
voltage.
939
2015 IEEE PES Innovative Smart Grid Technologies Latin America (ISGT LATAM)
PCC
PV Array
Cdc
Boost
dc
F
ZG Grid
dc
dc
ipv
Nonlinear
load
Inverter
ac
vdc
vpv
iS
vPCC
1. Grid-connected photovoltaic system based on multifunctional inverter.
ipv
Vpv
MPPT
*
Vpv
iind
*
PI
PI
PWM
(a)
VPCC
pcc
V
*
Vdc
PI
Vdc
SOGI-PLL
SOGI-PLL
i*
cos(θn)
θ *
i*S(t)
i (t)
iS(t)
iG(t)
* (t)
ihL
Harmonic
Detection
PI
V*
3. Current harmonic detection proposed based on SOGI-PLL.
The detection strategy is based on cascaded association
of two phase-locked loops (PLL) based on second order
generalized integrator (SOGI), as shown in Fig. 3. The detailed
description about these structures are shown in [16], [17], [21],
[22].
The first stage consists to detect the load fundamental
current component inL (t). In steady state, the measured load
current iL (t) is filtered by SOGI tuned in the fundamental
frequency, detected by the PLL. This is done making iq = 0.
The complete SOGI-PLL structure for fundamental component
detection is shown in Fig. 4. As depicted in [16], the closedloop transfer functions of the SOGI are defined as:
iind
Vpv
F
F
iG
Control
Strategy
PWM
iS(t)
(b)
′
i
kωs
Hd (s) = L (s) = 2
iL
s + kωs + ω 2
2. Complete control strategy. (a) Boost control strategy. (b) Inverter
control strategy.
(1)
′
Hq (s) =
II. C ONTROL S TRATEGY
Complete control strategy is presented in Fig. 2. The MPPT,
used in the dc/dc boost converter control loop, maintains the
solar array delivering maximum power to the system at various
levels of solar irradiance and temperature. Operating principle
of this algorithm used is based on perturbation and observation
(P&O) method [20]. The dc/dc stage uses a current mode
control structure, which is detailed in Fig. 2(a).
Inverter control strategy is shown in Fig. 2(b). The PI compensator is used in the dc-bus voltage control. This compensator calculates the active current amplitude i∗ , which needs to
be injected into the power system. This signal is synchronized
with PCC voltage through SOGI-PLL structure [16], [17],
resulting in a sinusoidal waveform i∗ (t). This current reference
is added to load harmonic component detected, generating
the current reference i∗S (t). Finally, i∗S (t) is compared with
the inverter current. Another PI compensator calculates the
converter modulation index V ∗ .
Generally, loads in an installation are connected in different points and the direct measurement of its current can
be difficult. This work estimates the load current in terms
of inverter injected current and grid current, to ensure the
harmonic compensation of all loads connected to the PCC.
III. A DAPTIVE C URRENT H ARMONIC D ETECTION
M ETHOD
In order to compensate just one load harmonic current
component in an installation, this work proposes a detection
method able to detect the load harmonic current component
with higher amplitude.
qiL
kω 2
(s) = 2
iL
s + kωs + ω 2
(2)
where ω is the resonant frequency and k is a damping factor,
which is responsible for SOGI’s bandwidth, as detailed in the
bode diagrams shown in Fig. 5 and Fig. 6. It is observed in
this structure a bandpass filter characteristic, with adjustable
resonant frequency ω.
In the fundamental
component detection, the SOGI gain is
√
set to k = 2 which results in an optimal relationship between
the settling time and suppression of unwanted frequencies [17].
However, the current may have a high harmonic contents. For
this reason, the low order harmonics close to the fundamental
frequency can impact the SOGI-PLL performance. Therefore,
the PLL bandwidth is reduced and the low pass filters (LPF)
are used in the frequency and amplitude detection to avoid
these oscillations, as illustrated in Fig. 4.
The second loop stage consists to detect the harmonic
contents with higher amplitude in the load current i∗hL (t). In
order to ensure the rotation of the space phasor orthogonal
to the q-axis, another PLL should be adjusted to the new
signal and to extract the angle and frequency of the harmonic
component with higher amplitude of the load current. This
frequency is used as feedback to another SOGI and it provides
two quadrature signals filtered in this frequency. This process
eliminates the harmonics of low amplitude and detects the
angle and amplitude of the predominant harmonic. The structure of SOGI-PLL for harmonic component detection stage is
similar to Fig. 4.
Current fundamental component inL (t) is detected by the
following multiplication:
940
inL (t) = in,peak cos(θn )
(3)
2015 IEEE PES Innovative Smart Grid Technologies Latin America (ISGT LATAM)
77
Adaptive Filter
245
ωn
s
iq
i’L
s
qiL
SOGI
PI
αβ
1
dq
ω’
id
1
θn
s
V
ωn
ωn
[V]
1
k
LPF
in,peak
235
LPF
4. General structure of a single-phase phase-locked loop (PLL).
%$#!"!
B()* +,-./-0
M
0
230
V
[V]
−20

−40
k21k233451
90
'&P
45
0
1
−45
−90
3
4
5
6
1
2
10
w
3
%!$#"!
420
419
1
2
3
4
5
6
7
8
Time [ s ]
(b)
IV. R ESULTS
−20
6
−40
k21k233451
−60
0
−45
−90
−135
1
421
10
B()* +,-./-0
1
dc
7. (a) Voltage at maximum power point of the solar plant. (b) Inverter
dc-bus voltage.
0
−180
*
dc
Frequency (rad/s)
20
M
8
77
422
417
4
10
pv
7
Time [ s ]
(a)
423
418
Fig. 5. Bode diagram of Hd .
&P
2
424
%"!#"
%"#!"'
1
425
dc
id2 + iq2
240
*
pv
pv
iL(t)
2
10
w
3
10
4
10
Frequency (rad/s)
Fig. 6. Bode diagram of Hq .
The PLL used in the harmonic component detection loop
has wide bandwidth in order to obtain fast stabilization in
the angle and frequency detection. However, the SOGI is set
to narrow bandwidth (k = 0.4), which results in an optimal
suppression of unwanted frequencies.
Furthermore, a LPF is used to support in the suppression the
oscillations. Therefore, the harmonic component with higher
amplitude in the load current i∗hL (t) is detected by 4. This
detected signal is sent to the control strategy for harmonic
compensation.
i∗hL (t) = ih,peak cos(θh ).
(4)
The case study presents a solar array with 5 parallel strings
of 13 panels of 48 W in series. The inverter rated power is
4kVA , which corresponds to 30% of overload capability. The
boost and inverter switching frequency is 12 kHz. Voltage at
point of common couple is 220 V. The discrete simulation was
implemented in Matlab/Simulink environment with sample
time of twice the switch frequency.
The solar irradiance is maintained in 500 W /m2 during the
study. The solar array voltage profile (Vpv ) is illustrated in
Fig. 7(a). This voltage tracks the maximum power point due
to MPPT algorithm presents in the boost converter control
strategy. The inverter dc-bus voltage (Vdc ) is controlled in 420
V as detailed in Fig. 7(b).
The nonlinear loads connected to the PCC are represented
by current sources, injecting harmonics in the system. In the
simulation, the load current harmonic contents are changed to
validate the new harmonic detection method proposed. The
load current contents during the time intervals are shown in
the spectrum in Fig. 8. Between 0 < t < 2s, the load current
harmonic contents has 5th and 7th harmonic with amplitude
of 3 A and 1 A, respectively (Fig. 8(a)). Between 2 ≤ t < 4,
the load current has a 5th and 7th harmonic of 1 A and 5 A,
respectively (Fig. 8(b)). Between 4 ≤ t < 6, the load harmonic
contents has a 5th and 7th harmonic, both with amplitude of 2
A (Fig. 8(c)). Between 6 ≤ t ≤ 8, the load current has a 3rd,
5th and 7th harmonic with amplitude of 6 A, 2 A and 0.5A,
respectively (Fig. 8(d)).
The amplitude of the load fundamental current is maintained
at 20 A in both cases. The fundamental component of the
detected load current is illustrated in Fig. 9. As the funda-
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2015 IEEE PES Innovative Smart Grid Technologies Latin America (ISGT LATAM)
4
1
0
0
5
7
1 2
3
1
0
9 11 13 15 17 19
(a)
4
8
0
0
5
7
Amplitude [A]
Amplitude [A]
1
5
7
1 2
4
9 11 13 15 17 19
1 2
4
2
0
9 11 13 15 17 19
(c)
−2
0
5
7
9 11 13 15 17 19
(d)
−6
Frequency [ Hz ]
60
G
0
1
2
3
TIJKL N O
4
5
6
7
8
(a)
25
20
15
10
G
5
0
1
2
3
TIJKL N O
4
3.002
RSUWXYZ
3.003
3.004
3.005
3.006
3.007
420
e
300
180
40
20
3.001
10. Details on the 7th harmonic of the load current and details on the
signal detected and rebuilt.
Amplitude [ A ]
Frequency [ Hz ]
Q
−4
1 2
80
Amplitude [ A ]
0
10
8. Load current spectrum, illustrating the changes in the harmonic
contents for the validation of the harmonic detection method proposed. (a)
Between 0 < t < 2 seconds. (b) Between 2 ≤ t < 4 seconds. (c) Between 4
≤ t < 6 seconds. (d) Between 6 ≤ t ≤ 8 seconds.
2
20
6
10
2
0
6
(b)
20
3
E
8 H9:;<=>?@:CD:
E
8 H9:;<=>?@:CD:
10
[A]
2
[\d^\]Uc[\^_S]`UaW^_bSW``bWc
8
20
7H
10
Amplitude [A]
Amplitude [A]
5
I
E
8 H9:;<=>? @:CD:
E
8 H9:;<=>? @:CD:
20
3
1
2
3
5
6
7
8
RSUWX Y Z
5
6
7
8
4
(a)
7
6
5
4
3
2
e
RSUWX Y Z
0
1
2
3
4
(b)
11. Harmonic component with higher amplitude detected of the load
current. (a) Signal frequency. (b) Signal amplitude.
5
6
7
8
(b)
9. Fundamental component of the load current detected. (a) Signal
frequency. (b) Signal amplitude.
mental component is not changed, the detected frequency and
amplitude are constants during the simulation, as shown in
Fig. 9(a) and Fig. 9(b), respectively. The detected amplitude
and frequency of the load harmonic component with higher
amplitude is illustrated in Fig. 11. The harmonic compensation
is enabled at 1 second. Initially, the 5th harmonic is detected.
Between 2 ≤ t ≤ 4 seconds the 7th is detected. Between 4 ≤
t < 6 seconds the 5th and 7th harmonic of the load current
have the same amplitude. For this reason, as the detector was
already tracking the 7th the detector PLL still locked for the
7th. Between 6 ≤ t ≤ 8 seconds the 3rd is detected as harmonic
with higher amplitude in the load current contents.
The detected harmonic is reconstructed and used by the
current control to perform the harmonic compensation. Details
on the detected 7th harmonic and its reconstruction are shown
in Fig. 10.
The compensation of the harmonic with higher amplitude in
the load current contents can greatly improve the grid power
quality with reduced control algorithm complexity. Details
of the grid current (iG ) and inverter current (iS ) when the
harmonic compensation is enabled in 1 second are shown in
Fig. 12(a) and Fig. 12(b), respectively.
The Fig. 12(c) shows the spectrum of the grid and inverter
current during the harmonic compensation between 1 ≤ t < 2
seconds. Note the suppression of the 5th harmonic in the grid
current.
Between 2 ≤ t < 6 seconds, the 7th harmonic of the load
current is strongly reduced in the grid current, as shown in
Fig. 12 and Fig. 13. After 6 seconds, the 3rd harmonic of the
load current is compensated, as detailed in Fig. 14.
The Table I details the total harmonic distortion (THD)
of the grid, inverter and load current during the harmonic
compensation. The Table II details the currents THD for the
same simulation without harmonic compensation. Note that,
the strongly improvement of the grid power quality index.
Between 6 ≤ t ≤ 8, e.g., the grid current THD reduces of
54.84 % (Table II) to 19.06 % (Table I).
942
2015 IEEE PES Innovative Smart Grid Technologies Latin America (ISGT LATAM)
0
−20
20
fghi
0.96
0.98
iG[ A ]
iG[ A ]
20
jlmno p q
1
1.02
1.04
1.06
1.08
1.1
−20
1.12
(a)
Amplitude [A]
−20
3
1
0
0.96
0.98
1
iS[ A ]
fghi
jlmno p q
1.04
1.06
1.08
1.1
1.12
(b)
10
r
5
0
5
7
9
1 2
11
13
15
17
19
(c)
†gh‡
2
jlmno p q
2.05
2
0
2.1
2.15
2.2
0
−20
2.25
(a)
4.15
4.2
4.25
rgh‡
4
jlmno p q
|x„u}nl{u~n€u €u nuxn~x‚ƒ~ ‚nƒyn~uy~mum
stumvxly zu{nu
4.05
4.1
4.15
4.2
4.25
(b)
r
5
0
5
7
1 2
9
11
13
15
17
19
(c)
‡gh‡
6
6.05
6.1
jlmno p q
6.15
6.2
6.25
6.3
6.35
(a)
†gh‡
2
IS[ A ]
20
jlmno p q
|x„u}nl{u~n€u €u nuxn~x‚ƒ~ ‚nƒyn~uy~mum
stumvxly zu{nu
2.05
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2.15
2.2
−20
2.25
Amplitude [A]
10
r
0
(b)
5
1
0
4.1
(a)
20
IG[ A ]
iG[ A ]
iS[ A ]
Amplitude [A]
−20
jlmno p q
4.05
10
4
20
0
4
14. (a) Grid current detail in 4 seconds. (b) Inverter current detail in 4
seconds. (c) Spectrum of inverter and grid current between 4 ≤ t < 6 seconds.
20
−20
0
−20
|x„u}nl{u~n€u €u nuxn~x‚ƒ~ ‚nƒyn~uy~mum
stumvxly zu{nu
1.02
12. (a) Grid current detail when the harmonic compensation is enabled
in 1 second. (b) Inverter current detail in 1 second. (c) Spectrum of inverter
and grid current between 1 ≤ t < 2 seconds.
0
rgh‡
20
Amplitude [A]
iS[ A ]
20
0
0
5
0
5
7
9
1 2
11
13
15
17
19
(c)
13. (a) Grid current detail in 2 seconds. (b) Inverter current detail in 2
seconds. (c) Spectrum of inverter and grid current between 2 ≤ t < 4 seconds.
4
2
0
6
6.05
jlmno p q
|x„u}nl{u~n€u €u nuxn~x‚ƒ~ ‚nƒyn~uy~mum
stumvxly zu{nu
6.1
6.15
6.2
6.25
6.3
6.35
(b)
10
r
5
0
5
7
9
1
2
11
13
15
17
19
(c)
15. (a) Grid current detail in 6 seconds. (b) Inverter current detail in 6
seconds. (c) Spectrum of inverter and grid current between 6 ≤ t ≤ 8 seconds.
V. C ONCLUSION
This work presented a novel adaptive current harmonic detection method applied in multifunctional single-phase photovoltaic inverters. This method consists in a cascade association
of two phase-locked loop based on second order generalized
integrator (SOGI-PLL).
The proposed strategy is frequency adaptive and able to detect the load current harmonic with higher amplitude. Thereby,
the current controller can be tuned for specific harmonics,
increasing efficiency and reducing the control algorithm complexity.
Simulation results showed the current harmonic detection
proposed method performance, which provided partial harmonic compensation.
6
‡gh‡
TABLE I
T OTAL C URRENT H ARMONIC D ISTORTION D URING H ARMONIC
C OMPENSATION
Intervals
0<t<1
1≤t<2
2≤t<4
4≤t<6
6≤t<8
THD iG (%)
27.83
9.9
10.72
19.73
19.06
THD iS (%)
1.18
35.57
60.89
24.64
72.83
THD iL (%)
15.69
15.69
25.39
14.02
31.48
The load connected at the point of common couple of the
case study presented 3rd, 5th and 7th harmonic. The harmonic
with higher amplitude was compensated and the results suggest improvements in the grid power quality indexes.
943
2015 IEEE PES Innovative Smart Grid Technologies Latin America (ISGT LATAM)
ˆ‰Š‹Œ
T OTAL C URRENT H ARMONIC D ISTORTION W ITHOUT H ARMONIC
C OMPENSATION
Intervals
0<t<1
1≤t<2
2≤t<4
4≤t<6
6≤t<8
THD iG (%)
27.83
28.23
45.70
24.95
54.84
THD iS (%)
1.18
1.20
1.17
1.15
1.30
THD iL (%)
15.69
15.69
25.39
14.02
31.48
ACKNOWLEDGMENT
The authors would like to thank the Brazilian agencies
CAPES, FAPEMIG and CNPQ, which supported this work.
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